This invention relates to a simulation technology and, more particularly, to a method for predicting a pattern width on a semiconductor wafer and a method for correcting a mask pattern on the basis of the result.
A pattern transfer is an important step in a process for fabricating a semiconductor device. Photo-resist is spread over a semiconductor wafer, and a photo mask is aligned with an area of the semiconductor wafer. The photo mask is radiated with light, and the light carries the pattern image onto the area. A latent image is produced in the photo mask, and is developed in developing solution. Then, the photo-resist layer is formed into a photo-resist pattern. If the photo-resist is of the positive type, part of the area irradiated with the light becomes soluble in the developing solution, and is removed from the semiconductor wafer. The remaining part of the photo-resist layer is left on the semiconductor wafer as the photo-resist pattern.
The pattern to be formed in the photo-resist layer has been miniaturized. When the pattern is miniaturized, the photo-resist pattern is degraded, and the pattern accuracy is lowered. The degradation is not uniform between sorts of pattern such as, for example, a line-and-space pattern, an isolated pattern etc. The phenomena influential in the pattern accuracy is hereinbelow referred to as xe2x80x9coptical proximity effectxe2x80x9d.
The optical proximity effect on the photo-resist pattern is variable depending upon the environments of the pattern transfer such as exposure conditions, i.e., the aberration, the defocus, the dimensional error in the mask pattern and so forth, the developing time and the design method for the mask pattern. In order to exactly design a photo mask, the manufacturer simulates the pattern transfer, and predicts the photo-resist pattern on a semiconductor wafer. Then, the manufacturer feeds back the prediction to the design work for an optical proximity correction, and corrects the photo mask pattern. Thus, the prediction through the simulation is an important technology for the work of designing a photo mask.
A problem is encountered in the prior art in that the prediction is time consuming. The analyst takes the pattern dimensions and sorts of the pattern, which are influenceable by the thickness of a photo-resist layer and the composition of photo-resist, into account, and the simulation requires complicated calculations for the prediction. Moreover, the analyst requires a large amount of experimental data for pattern transfer under different conditions in order to obtain resist patterns at a predetermined depth of focus. The experiments are also time consuming and costly.
It is therefore an important object of the present invention to provide a method for accurately speedily predicting a pattern width.
It is also an important object of the present invention to provide a method for correcting a mask pattern on the basis of the prediction.
In accordance with one aspect of the present invention, there is provided a method for predicting a width of a pattern transferred from a photo-mask to a photo-sensitive layer comprising the steps of a) determining a first optical intensity at first positions on the photo-sensitive layer corresponding to edges of the photo-mask and a second optical intensity at a second position where the optical intensity is predicted to be weaker than the first optical intensity on the basis of a first spatial image of the pattern calculated under reference exposure conditions, b) determining a distance between third positions approximately equal in optical intensity to the first positions and a third optical intensity at a fourth position corresponding to the second position on the basis of a second spatial image of the pattern calculated under actual exposure conditions and c) predicating the width of the pattern formed in the photo-sensitive layer on the basis of the distance, the second optical intensity and the third optical intensity.
In accordance with another aspect of the present invention, there is provided a method for correcting a pattern to be transferred from a photo-mask to a photo-sensitive layer comprising the steps of a) determining a first optical intensity at first positions on the photo-sensitive layer corresponding to edges of the photo-mask and a second optical intensity at a second position where the optical intensity is predicted to be weaker than the first optical intensity on the basis of a first spatial image of the pattern calculated under reference exposure conditions, b) determining a distance between third positions approximately equal in optical intensity to the first positions and a third optical intensity at a fourth position corresponding to the second position on the basis of a second spatial image of the pattern calculated under actual exposure conditions, c) predicating the width of the pattern formed in the photo-sensitive layer on the basis of the distance, the second optical intensity and the third optical intensity, d) comparing the width predicated at step c) with a target width to see whether or not the pattern on the photo-mask is appropriate and e) redesigning the photo-mask when the answer at step d) is given negative.